Explanation Given Information: In Morse code, each letter of the alphabet is encoded by a different sequence of dots and dashes and different letters may have different lengths. Formula used: The Decision Algorithm is to make a set of decisions to determine the number of possible outcomes. The Multiplication Principle, if there is a sequence of choice with r disjoint steps and step 1 has n 1 possible outcomes, step 2 has n 2 possible outcomes and so on and step r has n r possible outcomes with no two outcomes same, then the total number of outcomes are n 1 × n 2 × … × n r . Calculation: Consider in Morse code, each letter of the alphabet is encoded by a different sequence of dots and dashes and different letters may have different lengths. Use the Decision Algorithm to make a set of decisions to determine the number of possible outcomes. Consider the Decision Algorithm, choose the number of sequences. Since, the sequences consists of dots and dashes, there are 2 choices. Alternative 1: Consider sequence of length 1. Since, the sequences consist of dots and dashes, the length 1 sequence either is a dot or a dash. Thus, Alternative 1 has 2 choices. Alternative 2: Consider sequence of length 2. Step 1: Choose a dot or a dash for the first empty slot. Thus, Step 1 has 2 choices. Step 2: Choose a dot or a dash for the second empty slot. Thus, Step 2 has 2 choices. Alternative 3: Consider sequence of length 3. Step 1: Choose a dot or a dash for the first empty slot. Thus, Step 1 has 2 choices. Step 2: Choose a dot or a dash for the second empty slot. Thus, Step 2 has 2 choices. Step 3: Choose a dot or a dash for the third empty slot. Thus, Step 3 has 2 choices. Alternative 4: Consider sequence of length 4. Step 1: Choose a dot or a dash for the first empty slot. Thus, Step 1 has 2 choices. Step 2: Choose a dot or a dash for the second empty slot. Thus, Step 2 has 2 choices. Step 3: Choose a dot or a dash for the third empty slot. Thus, Step 3 has 2 choices. Step 4: Choose a dot or a dash for the fourth empty slot. Thus, Step 4 has 2 choices. Consider Alternative 2. Use the Multiplication Principle, if there is a sequence of choice with r disjoint steps and step 1 has n 1 possible outcomes, step 2 has n 2 possible outcomes and so on and step r has n r possible outcomes with no two outcomes same, then the total number of outcomes are n 1 × n 2 × … × n r . Since, there are 2 steps, r = 2 and no two are same. Thus the total number of choices is, n 1 × n 2 = 2 × 2 = 4 Thus, Alternative 2 has 4 choices. Consider Alternative 3

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Chapter 7.3, Problem 65E

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To calculate: The length of the longest sequence to allow for every possible letter of the alphabet where in Morse code, each letter of the alphabet is encoded by a different sequence of dots and dashes and different letters may have different lengths.

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Chapter 7.3, Problem 64E

Chapter 7.3, Problem 66E

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EBK FINITE MATH AND APPLIED CALCULUS

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

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The length of the longest sequence to allow for every possible letter of the alphabet where in Morse code, each letter of the alphabet is encoded by a different sequence of dots and dashes and different letters may have different lengths.

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To calculate: The length of the longest sequence to allow for every possible letter of the alphabet where in Morse code, each letter of the alphabet is encoded by a different sequence of dots and dashes and different letters may have different lengths.

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